Variable displacement multi-chamber pumps are known in the art. However, these pumps typically have shortcomings, such as leakage issues between the control ring and housing and a limited range of pressure outputs. Examples of such pumps are disclosed in U.S. 2009/0196780 A1, U.S. 2010/0329912 , U.S. Pat. Nos. 8,057,201, 7,794,217, 4,678,412, each of which is incorporated herein in their entirety.